Distributional Clustering: A distribution-preserving clustering method
This addresses a drawback in clustering for tasks requiring representative points that mimic data distributions, though it appears incremental as it builds on k-means.
The paper tackles the problem of k-means cluster centers distorting data distributions, proposing distributional clustering to ensure centers capture the underlying data distribution, and demonstrates its effectiveness on synthetic and real datasets.
One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the distribution of the underlying data. This can be highly disadvantageous in problems where the representative points are subsequently used to gain insights on the data distribution, as these points do not mimic the distribution of the data. To this end, we propose a new clustering method called "distributional clustering", which ensures cluster centers capture the distribution of the underlying data. We first prove the asymptotic convergence of the proposed cluster centers to the data generating distribution, then present an efficient algorithm for computing these cluster centers in practice. Finally, we demonstrate the effectiveness of distributional clustering on synthetic and real datasets.